Question

One leg of a right triangle measures 6 inches. The remaining leg measures 6√3 inches. What is the measure of the angle opposite the leg that is 6 inches long?

Answer 1

30°
Here's why:
Using the well-known Pythagorian theorem we can reckon how long the hypotenuse is:
c^2=6^2+36*3 -> c=12
Knowing that sin(a)=a/c=6/12=0.5 the measure of the angle in degrees is 30°
Hope could help :)

Answer 2

Answer:

30°

Step-by-step explanation:

One leg of a right triangle measures 6 inches.

Leg 1 (Opposite) = 6

The other leg measure $6\sqrt{3}$ inches.

Leg 2 (Base ) = $6\sqrt{3}$

Let the measure of angle opposite of the leg 6 inches be Ф

Using trigonometry identity

$\tan\theta=\dfrac{\text{Opposite}}{\text{Base}}$

$\tan\theta=\dfrac{6}{6\sqrt{3}}$

Cancel 6 from top and bottom

$\tan\theta=\dfrac{1}{\sqrt{3}}$

$\theta=\tan^{-1}(\frac{1}{\sqrt3})$

$\theta=30^\circ$

Hence, The measure of opposite angle of leg 6 inches is 30°